Two components in bipolar scales: Direction and extremeness

Various measures in psychology use a set of response categories extending in two directions about some neutral point. Scores for several responses are summed or averaged to give a composite score. Examples would include some of the methods of absolute judgment in psychophysics, the Likert-type of attitude scale, Osgood's semantic differential, rating scales used in personality assessment. The object of measurement for the composite scores may thus be some attribute of physical stimuli, of verbal concepts, of other persons, or of oneself. Two components can be distinguished in the responses: (a) the direction from the neutral point, representing the basic dichotomy--heavy versus light, agreement versus disagreement with the statement, etc.; (b) the degree or extremeness of the response from the neutral point. For example, in a six-point Likert scale the subject writes + 1, + 2, + 3; or - 1, - 2, - 3 to indicate slight, moderate, and strong agreement or slight, moderate, and strong disagreement. The basic dichotomy of direction is determined by whether he agrees or disagrees (writes + or -); extremeness by whether he indicates slight, moderate, or strong feelings (writes 1, 2, or 3). A neutral response category may or may not be provided--e.g., Likert scales traditionally permitted a neutral response (writing 0), but many recent Likert scales do not. When scores for several responses are summed or averaged to give a composite score, the two components become: the number (more generally, the proportion) of responses scored in each direction; the mean extremeness of the responses in each direction. The present paper derives a method for estimating the relative contribution of these two components to composite scores, and applies the method to data from several Likert attitude scales.